Precalculus Examples

$\log_{3} (\frac{x^{2}}{y^{7}})$

Step 1

Rewrite $\log_{3} (\frac{x^{2}}{y^{7}})$ as $\log_{3} (x^{2}) - \log_{3} (y^{7})$ .

$\log_{3} (x^{2}) - \log_{3} (y^{7})$

Step 2

Expand $\log_{3} (x^{2})$ by moving $2$ outside the logarithm.

$2 \log_{3} (x) - \log_{3} (y^{7})$

Step 3

Expand $\log_{3} (y^{7})$ by moving $7$ outside the logarithm.

$2 \log_{3} (x) - (7 \log_{3} (y))$

Step 4

Multiply $7$ by $- 1$ .

$2 \log_{3} (x) - 7 \log_{3} (y)$